Samantha Harvey continues to confound expectations. Her first novel, 2009's The Wilderness, explored the mind of a retired widower grappling with Alzheimer's disease. The understated and fractured narrative made the book a difficult read at times, and yet, by the end of it, one felt one had experienced a life. It went on to be longlisted for the Man Booker, shortlisted for the Orange prize and the Guardian first book award, and to win a Betty Trask prize.

Harvey's second novel, All Is Song, was, if anything, even more understated. She stuck with the third-person narrator, with characters many years her senior, and with male protagonists, two brothers. She painted miniature portraits in painstaking detail, but the tiny canvases – or maybe it was the reduced palette – limited the novel to a degree.

Dear Thief, Harvey's atmospheric third novel, denotes a major shift in gear. Harvey has switched gender and pronoun. Here she uses a first-person female narrator, addressing herself to the eponymous thief, who is narrated in the second person: "You pitched your ragged beauty on our windowsill like a makeshift tent; really you never did look like somebody who was going to be there long."

The novel is presented as a long letter, a literary device that is difficult to pull off, but Harvey's innovations electrify every word. The plot details a love triangle. A middle-aged woman (for Harvey has remained loyal to her ageing characters, and to the topic of ageing in general) sits down the night after Christmas to write to her absent friend-turned-foe, the woman who stole her husband and their future together. She addresses this treasured and abhorred old friend by her pet name, Butterfly. Butterfly, we gradually find out, has not been seen in years. Butterly is fragile, but also lethal. She is exotic and fearless and selfish and dangerous, a wholly fascinating invention – invention being the operative word, because the Butterfly we are introduced to is, essentially, the invention of the letter-writer, who must narrate her in her absence. She no longer knows where Butterfly is, whether she is even alive, and so she writes to – and about – "this tentative, hypothesised you". All this is set against the backdrop of the final days of Soviet control of Lithuania, where Butterfly's family is from.

In the voice of a middle-aged woman looking back over her marriage, Harvey has struck gold. It is an educated and meditative voice, reminiscent of those deployed by great stylists such as WG Sebald, Claire Messud, John Banville and Joseph O'Neill. Why is this voice so evocative, I found myself wondering. Why is it (literally, as it happens) striking a chord? The answer is Leonard Cohen.

Dear Thief is a novelisation of Cohen's "Famous Blue Raincoat", a song about a love triangle, which is also presented as a letter to the third party who broke up a marriage. Both letters are started at four in the morning at the end of December. Harvey's narrator sits at a desk in Goodge Street, London, not Clinton Street, New York. It's cold and she is no longer in the family home, but she likes her apartment – there's music all evening from the jazz bar down the road. Butterfly wears a shawl, which over the years becomes filthy and torn at the shoulder, like the blue raincoat of Cohen's song. Both letter-writers wonder whether their old friend is better yet, for both the marriage-wreckers have demons. Both are now living in a house in the desert. And, of course, there is the lock of hair.

This is not to say that Dear Thief achieves its emotional power because of the song – I connected the two some time after I had finished the book. The novel had left an imprint in its own right. Dear Thief is written in the same key as the song – a minor and melancholic one, which captures a heady, elegiac combination of eroticism and loss, loathing and rapture, the messy complexity of a spurned woman's emotional landscape. Harvey's narrator watches her beloved friend seduce her husband – "somebody we love has loved someone else more, and we feel swiped aside like a skittle" – and although she is unable to forgive her friend for stealing her future, she is unable to stop caring about her either.

In most books, events happen solely on the page. In the best books, events happen in the reader, too. Perhaps because it is so intimate, so honest, so raw, Dear Thief provokes you to think about life, and Life, and your own life, the people in it as well as the ghosts.

• Claire Kilroy's The Devil I Know is published by Faber. To order Dear Thief for £13.59, go to bookshop.theguardian.com or call 0330 333 6846.